Advances in Differential Equations

Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term

Nam Q. Le

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Abstract

In this paper, we show that critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term converge to those of the corresponding Mumford-Shah functional, a famous model for image segmentation. Equi-partition and convergence of the energy-density are also derived.

Article information

Source
Adv. Differential Equations Volume 15, Number 3/4 (2010), 255-282.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854750

Mathematical Reviews number (MathSciNet)
MR2588770

Zentralblatt MATH identifier
1190.49048

Subjects
Primary: 49Q20: Variational problems in a geometric measure-theoretic setting 49J45: Methods involving semicontinuity and convergence; relaxation 35B38: Critical points 35J60: Nonlinear elliptic equations

Citation

Le, Nam Q. Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term. Adv. Differential Equations 15 (2010), no. 3/4, 255--282. https://projecteuclid.org/euclid.ade/1355854750.


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